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Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, estimate of the self-inductance of the circuit is
  • a)
    4H .
  • b)
    5H
  • c)
    2H
  • d)
    3H
Correct answer is option 'A'. Can you explain this answer?
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Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average...
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Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average...
Given:
- Current (I) falls from 5.0 A to 0.0 A
- Time taken (t) = 0.1 s
- Average induced emf (e) = 200 V

To find:
- Self-inductance (L) of the circuit

Formula:
- Induced emf (e) = -L(dI/dt)

Explanation:

Finding dI/dt:

- Initial current, I1 = 5.0 A
- Final current, I2 = 0.0 A
- Time taken, t = 0.1 s

dI/dt = (I2 - I1) / t
= (0.0 - 5.0) / 0.1
= -50 A/s

Finding L:

e = -L(dI/dt)

L = -e/(dI/dt)

Substituting the given values,

L = -200 V / (-50 A/s)
= 4 H

Therefore, the self-inductance of the circuit is 4 H.

Conclusion:
The correct option is (a) 4H.
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Read the following text and answer the following questions on the basis of the same: TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.Why inductance of solenoid is more than the inductance of a solenoid having same number of turns, core of same material and similar size?

Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, estimate of the self-inductance of the circuit isa)4H .b)5Hc)2Hd)3HCorrect answer is option 'A'. Can you explain this answer?
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